University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
Motion of Particles under Pseudo-Deformation
273
277
EN
Akhilesh
Chandra
Yadav
M G Kashi Vidyapith Varanasi
akhileshyadav538@gmail.com
10.22052/mir.2016.34108
In this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{A}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. We also observe that the effective force $mathbf{F}_e$ on that particle due to pseudo-force $mathbf{A}(t)$, is given by $ mathbf{F}_e= mathbf{F} mathbf{A}(t)+ mathbf{L} dmathbf{A}(t)/dt$, where $mathbf{F}= m d^2mathbf{r}/dt^2 $ and $mathbf{L}= m dmathbf{r}/dt$. We have discussed stream lines under pseudo-force.
Right loops,right transversals,gyrotransversals
http://mir.kashanu.ac.ir/article_34108.html
http://mir.kashanu.ac.ir/article_34108_1020df1e5666b6a0fea4c5f804264b84.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
C-Class Functions and Remarks on Fixed Points of Weakly Compatible Mappings in G-Metric Spaces Satisfying Common Limit Range Property
279
290
EN
Arslan
Hojat Ansari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran,
analsisamirmath2@gmail.com
Diana
Dolicanin-Dekic
Faculty of Technical Science, 38000 Kosovska Mitrovica,
dolicanin_d@yahoo.com
Feng
Gu
Institute of Applied Mathematics and
Department of Mathematics,
Hangzhou Normal University, Hangzhou, Zhejiang 310036,
gufeng99@sohu.com
Branislav
Popovic
4Faculty of Science, University of Kragujevac, Radoja Domanovica 12, 34000 Kragujevac, Serbia,
bpopovic@kg.ac.rs
Stojan
N
Radenovic
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
radens@beotel.rs
10.22052/mir.2016.34106
In this paper, using the contexts of C-class functions and common limit<br />range property, common fixed point result for some operator are obtained.<br />Our results generalize several results in the existing literature. Some examples<br />are given to illustrate the usability of our approach.
Generalized metric space,common fixed point,generalized weakly G-contraction,weakly compatible mappings,common (CLRST ) property,C-class functions
http://mir.kashanu.ac.ir/article_34106.html
http://mir.kashanu.ac.ir/article_34106_f7148aa5b4661811ab50e7cd0cffd3d4.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation
291
304
EN
Akbar
Mohebbi
University of Kashan
a_mohebbi@kashanu.ac.ir
Zahra
Faraz
University of Kashan
zahrafaraz44@yahoo.com
10.22052/mir.2016.15512
In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method. In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method. In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method.
Finite difference scheme,solvability,unconditional stability,Convergence
http://mir.kashanu.ac.ir/article_15512.html
http://mir.kashanu.ac.ir/article_15512_124ceee6f307b4edb7a77d6025a2e5e1.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
Wiener Polarity Index of Tensor Product of Graphs
305
316
EN
Mojgan
Mogharrab
Persian Gulf University
mmogharab@gmail.com
Reza
Sharafdini
Persian Gulf University
sharafdini@gmail.com
Somayeh
Musavi
Mathematics House of Bushehr
smusavi92@gmail.com
10.22052/mir.2016.34109
Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index of a graph G is denoted by W_P (G) is the number of unordered pairs of vertices of distance 3. The Wiener polarity index is used to demonstrate quantitative structure-property relationships in a series of acyclic and cycle-containing hydrocarbons. Let G,H be two simple connected graphs. Then the tensor product of them is denoted by G⨂H whose vertex set is V(G⨂H)=V(G)×V(H) and edge set is E(G⨂H)={(a,b)(c,d)| ac∈E(G) ,bd∈E(H) }. In this paper, we aim to compute the Wiener polarity index of G⨂H which was computed wrongly in [J. Ma, Y. Shi and J. Yue, The Wiener Polarity Index of Graph Products, Ars Combin., 116 (2014) 235-244].
topological index,Wiener polarity index,tensor product,Graph,Distance
http://mir.kashanu.ac.ir/article_34109.html
http://mir.kashanu.ac.ir/article_34109_2979030b6f901a9245e59b804f53aab3.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
Diameter Two Graphs of Minimum Order with Given Degree Set
317
323
EN
Gholamreza
Abrishami
Ferdowsi University of Mashhad
gh.abrishamimoghadam@stu.um.ac.ir
Freydoon
Rahbarnia
Ferdowsi University of Mashhad
rahbarnia@um.ac.ir
Irandokht
Rezaee
Ferdowsi University of Mashhad
iran_re899@yahoo.com
10.22052/mir.2016.34107
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for a given set of natural numbers greater than one, we determine the minimum order of a 2-self-centered graph with that degree set.
Degree set,self-centered graph,radius,diameter
http://mir.kashanu.ac.ir/article_34107.html
http://mir.kashanu.ac.ir/article_34107_f8c714c2b1ea6bcadfdfe4ef88683da2.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
1
2
2016
07
01
Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
325
334
EN
Seyfollah
Mosazadeh
University of Kashan
s.mosazadeh@kashanu.ac.ir
10.22052/mir.2016.33850
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem. Finally, by the sequence of orthogonal eigenfunctions, we provide the eigenfunction expansions for twice continuously differentiable functions.
Boundary value problem,Eigenvalue,eigenfunction,completeness,eigenfunction expansion
http://mir.kashanu.ac.ir/article_33850.html
http://mir.kashanu.ac.ir/article_33850_0af3a4d1236273501fd68bad66d189f3.pdf